Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4, 5	, ⊢
	: , : , : , :
2	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
3	instantiation	6, 7	⊢
	:
4	instantiation	8, 9, 10	, ⊢
	: , :
5	instantiation	11, 68, 54	, ⊢
	: , :
6	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
7	instantiation	12, 66, 63	⊢
	: , :
8	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
9	instantiation	69, 44, 13	⊢
	: , : , :
10	instantiation	21, 14, 15	, ⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
12	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
13	instantiation	69, 49, 16	⊢
	: , : , :
14	instantiation	37, 24, 17	, ⊢
	: , :
15	instantiation	18, 19, 20	, ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
17	instantiation	21, 22, 23	, ⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	29, 71, 25, 30, 27, 31, 24, 38, 39, 33	, ⊢
	: , : , : , : , : , :
20	instantiation	29, 30, 66, 25, 31, 26, 27, 34, 35, 38, 39, 33	, ⊢
	: , : , : , : , : , :
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	37, 28, 33	, ⊢
	: , :
23	instantiation	29, 30, 66, 71, 31, 32, 38, 39, 33	, ⊢
	: , : , : , : , : , :
24	instantiation	37, 34, 35	⊢
	: , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
26	instantiation	40	⊢
	: , :
27	instantiation	36	⊢
	: , : , :
28	instantiation	37, 38, 39	⊢
	: , :
29	theorem		⊢
	proveit.numbers.multiplication.disassociation
30	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	40	⊢
	: , :
33	instantiation	69, 44, 41	, ⊢
	: , : , :
34	instantiation	69, 44, 42	⊢
	: , : , :
35	instantiation	69, 44, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
37	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
39	instantiation	69, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41	instantiation	69, 47, 46	, ⊢
	: , : , :
42	instantiation	69, 47, 48	⊢
	: , : , :
43	instantiation	69, 49, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
46	instantiation	69, 52, 51	, ⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	69, 52, 62	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
51	instantiation	69, 53, 54	, ⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	55, 56, 57	⊢
	: , :
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
56	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
57	instantiation	58, 59, 60	⊢
	: , :
58	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
59	instantiation	61, 62, 63	⊢
	: , :
60	instantiation	64, 65	⊢
	:
61	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
62	instantiation	69, 70, 66	⊢
	: , : , :
63	instantiation	69, 67, 68	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	69, 70, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
68	assumption		⊢
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1